Fundamental Theory of Elasticity and Stress Analysis
| Numbering Code |
U-ENG23 33200 LJ77 U-ENG23 33200 LJ71 |
Year/Term | 2022 ・ First semester | |
|---|---|---|---|---|
| Number of Credits | 4 | Course Type | Lecture | |
| Target Year | Target Student | |||
| Language | Japanese | Day/Period | Mon.1・2 | |
| Instructor name |
TSUKADA KAZUHIKO (Graduate School of Engineering Professor) MURATA SUMIHIKO (Graduate School of Engineering Associate Professor) |
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| Outline and Purpose of the Course | Stress, strain, displacement, and basic equations in linear elasticity are first lectured, and then Airy's stress function and its application to solve two-dimensional problems in linear elasticity are explained. Moreover, energy theorems and their application to a numerical stress analysis method are described. | |||
| Course Goals | This course aims to master the basics to solve the boundary value problems in linear elasticity analytically or numerically and to obtain the basic knowledge of numerical stress analysis methods such as FEM and BEM. | |||
| Schedule and Contents |
1st: Explanation about the contents, schedule and evaluation etc. Outline of class and explanation of syllabus, History of elasticity, Stress, Coordinate transformation of stress, Principal stress 2nd: Maximum shear stress, Mohl’s stress circle, Invariant of stress 3rd: Displacement and strain, Coordinate transformation of strain, Invariant of strain, Mohl’s strain circle 4th: Relationship between stress and strain, Elastic modulus, Basic equations of elasticity in rectangular coordinate system, Elastic basic formula in polar coordinate system 5th: Airy's stress function in rectangular coordinate system, Two-dimensional elastic problem using Airy's stress function 6th: Various Airy’s stress function in rectangular coordinate system 7th: Airy's stress function in polar coordinate system, Two-dimensional elastic problem using Airy's stress function in polar coordinate system 8th: Two-dimensional elastic problem using Airy's stress function in polar coordinate system 9th: Intermediate examination 10th: Introduction of "Mechanical analysis for elastic bodies based on energy principle", Basic equations of small displacement problem in elasticity its solution 11th: Energy principle (Principle of virtual work / Complement virtual work, Strain energy function) 12th: Energy principle (Principle of minimum potential energy, Simple example of energy principle) 13th: Approximate solution based on the variational principle (Approximate solution based on the principle of virtual work and principle of minimum potential energy) 14th: Approximate solution based on variational principle (Introduction to finite element method) 15th: Finite element method for elastic problems, Feedback class |
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| Evaluation Methods and Policy | Several Exercises are presented in the term. The midterm exam and final exam are also given. The grade is evaluated by the sum of the exercises and the exams with the weight of 30% and 70%, respectively. | |||
| Course Requirements | Differential calculus, integral calculus, and linear algebra are necessary for taking this course. | |||
| Study outside of Class (preparation and review) | It is strongly recommended to solve again the example problems explained in the lecture by yourself. | |||
| Textbooks | Textbooks/References | Not specified. | ||
| References, etc. | Introduction of Mechanics of elasticity-from basic theory to numerical analysis-, Shigeo Takezono et al., (Morikita Publishing Co.), ISBN:9784627666412, in Japanese | |||
| Related URL | ||||
